Multiple scattering by discrete random media: a summation of planar diagrams

The multiple scattering of a scalar wave by a discrete random medium is considered. The scatterers are assumed to be isotropic, incorrelated, and distributed uniformly. The Feynman-diagram technique is used to formulate the problem, and the Dyson equation is derived with the occupation-number formalism. Among the terms of the mass operator, a topological class of ´planar diagrams´ is defined, excluding all the interactions involving the same particle three times or more. It is possible to achieve analytically the summation of such diagrams. The corresponding mean field is computed and compared with other approximations such as those of Born and Twersky. The result does not reduce to Twersky´s even in the case of small concentrations of scatterers.<>